Here is the full list of all 12 Cobalt Core achievements.
Unlock CAT.
Beat the finale.
Unlock the Tiderunner.
Win a run on the hardest difficulty.
Win a fight you shouldn't have started.
Unlock the Gemini.
Unlock Max.
Unlock Books.
Unlock the Jupiter.
Unlock Drake.
Unlock the Ares.
Unlock Isaac.